An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects

Leineweber, Daniel B.; Bauer, Irene; Bock, Hans Georg; Schlöder, Johannes P.

doi:10.1016/s0098-1354(02)00158-8

Cited by 322 publications

(171 citation statements)

References 10 publications

Supporting

Mentioning

170

Contrasting

Unclassified

Order By: Relevance

“…In the classical condensing algorithm [3,10] that works as a preprocessing step to obtain a small dense QP from the block sparse one, the matching conditions (9b) are used for block Gaussian elimination of the steps of the additionally introduced state variables (δ s 1 , . .…”

Section: Classical Condensingmentioning

confidence: 99%

Complementary Condensing for the Direct Multiple Shooting Method

Kirches

Bock

Schlöder

et al. 2012

Modeling, Simulation and Optimization of Complex Processes

Self Cite

View full text Add to dashboard Cite

Summary. In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning the solution of the quadratic subproblems we present a factorization of the QP's KKT system, based on a combined null-space range-space approach exploiting the problem's block sparse structure. We demonstrate the merit of this approach for a vehicle control problem in which the integer gear decision is convexified.

show abstract

Section: Classical Condensingmentioning

confidence: 99%

Complementary Condensing for the Direct Multiple Shooting Method

Kirches

Bock

Schlöder

et al. 2012

Modeling, Simulation and Optimization of Complex Processes

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section we briefly review this condensing algorithm due to [26,7] and presented to great detail in [24], and give an account of the runtime complexity of the various steps.…”

Section: Condensing To Obtain a Dense Quadratic Problemmentioning

confidence: 99%

“…, δs m ) from system (20), analogous to the usual Gaussian elimination method for triangular matrices. This elimination procedure was introduced in [7] and a detailed presentation can be found in [24]. From this elimination procedure the dense constraint matrix (21)…”

Section: Elimination Using the Matching Conditionsmentioning

confidence: 99%

Block-structured quadratic programming for the direct multiple shooting method for optimal control

Kirches

Bock

Schlöder

et al. 2011

Optimization Methods and Software

Self Cite

View full text Add to dashboard Cite

Abstract. In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using sequential quadratic programming methods. We review the classical condensing algorithm that preprocesses the large but sparse quadratic programs to obtain small but dense ones. We show that this approach leaves room for improvement when applied in conjunction with outer convexification. To this end, we present a new complementary condensing algorithm for quadratic programs with many controls. This algorithm is based on a hybrid null-space range-space approach to exploit the block sparse structure of the quadratic programs that is due to direct multiple shooting. An assessment of the theoretical run time complexity reveals significant advantages of the proposed algorithm. We give a detailed account on the required number of floating point operations, depending on the process dimensions. Finally we demonstrate the merit of the new complementary condensing approach by comparing the behavior of both methods for a vehicle control problem in which the integer gear decision is convexified.

show abstract

“…The state variables at the initial time of each subinterval become additional decision variables in the NLP problem, state continuity at the transition times is enforced by imposing extra constraints, and the rest of the approach remains analogous to single shooting. The multiple shooting approach is available in state-of-the-art optimal control software based on local optimization solvers [26,27], where the block structure of the NLP problem is exploited within the underlying linear algebra routines for efficiency. This approach has not been used in a global optimization context to date, presumably due to the fact that larger NLP problems are usually more difficult to solve using branch-and-bound search.…”

Section: Introductionmentioning

confidence: 99%

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

Houska

Chachuat

2013

J Optim Theory Appl

View full text Add to dashboard Cite

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example.

show abstract

An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects

Cited by 322 publications

References 10 publications

Complementary Condensing for the Direct Multiple Shooting Method

Complementary Condensing for the Direct Multiple Shooting Method

Block-structured quadratic programming for the direct multiple shooting method for optimal control

Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

Contact Info

Product

Resources

About